Cadmium telluride (CdTe) based solar cells have emerged in recent years as commercially successful second generation thin film photovoltaic (PV) products. Despite intensive research, however, the ratio of lab demonstrated light-to-electricity conversion efficiency has been low. For example, while CdTe based solar cells can have a theoretical conversion efficiency limit of about 29%, a conversion efficiency of only about 16.5% has been achieved in practice. Despite having a theoretical conversion efficiency limit that is higher than some other thin film technologies, the CdTe based solar cells tend to trail these thin film technologies in realized conversion efficiency. For example, cadmium indium gallium selenide (CIGS) based solar cells have a lower theoretical conversion efficiency limit of only about 26%, but a higher realized conversion efficiency of about 19.9%.
One of the reasons for this conversion efficiency discrepancy may be a low doping level or hole concentration of p-type CdTe (p-CdTe). It is often desired to have a p-type doping (p-doping) level on the order of about 1016 to 1017 cm−3. However, the p-doping level of CdTe is typically on the order of about 1014 cm−3. As a result, CdTe based solar cells typically experience lower junction band bending and difficulty with ohmic contact, both of which can contribute to a lower open circuit voltage (VOC), and therefore, a lower conversion efficiency.
The doping level of a semiconductor device can be dependent, at least in part, on the activation energy of the dopant and/or the localized impurity/defect mid-bandgap (midgap) electronic states (hereinafter “impurity/defect states”) of the doped semiconductor device. There are several approaches to classifying the impurity/defect states including dopant/deep level classification, shallow/non-shallow dopant classification, single-level/multi-level state classification, and states of single or multiple atomic configuration classification. These classification schemes can provide some insight regarding which impurity/defect states may be responsible for p-doping of CdTe polycrystalline thin film in a CdS/CdTe junction solar cell. By way of background, each of these classification schemes are described below.
Dopant and Deep Level Classification
Using the dopant and deep level classification scheme, localized states in the bandgap of a semiconductor are usually classified as either dopants or deep levels based on a proximity of their ionization energy levels to the band edge. The dopant dopes the semiconductor, determining its type (n or p), Fermi level, and majority carrier density. The deep levels may compensate the doping level of the dopants, but are mostly treated as Shockley-Read-Hall (SRH) generation-recombination centers, with negative impact on the performance of most devices, including solar cells.
The localized states can be defined as dopants if the ionization or activation energy levels associated with the localized states are less than 0.05 eV from the band edge, and as deep levels if greater than 0.05 eV. Such a classification and description of the localized states in a semiconductor is generally appropriate for most widely used semiconductor materials, such as Si and GaAs, which are usually intentionally doped with a single dominant dopant state of shallow energy level and inadvertently incorporate undesired deep levels with concentration typically at least one order lower than that of the dopant. For n-type and p-type doping under the dopant and deep level classification scheme, the electron density n and the hole density p can be expressed as follows:
                    {                                                            For                ⁢                                                                  ⁢                n                ⁢                                  -                                ⁢                type                                                                    n                ≈                                  N                  D                  +                                ≈                                  N                  D                                                                    or                                                      n                ≈                                                      N                    D                                    -                                      N                    A                                                                                                      with                ⁢                                                                  ⁢                acceptor                ⁢                                                                  ⁢                compensation                                                                                        For                ⁢                                                                  ⁢                p                ⁢                                  -                                ⁢                type                                                                    p                ≈                                  N                  A                  -                                ≈                                  N                  A                                                                    or                                                      p                ≈                                                      N                    A                                    -                                      N                    D                                                                                                                        with                  ⁢                                                                          ⁢                  donor                  ⁢                                                                          ⁢                  compensation                                ,                                                                        (        1        )            
where ND, ND+, NA, and NA− are the concentrations or densities of donors, ionized donors, acceptors, and ionized acceptors, respectively.
Such a classification of states is not appropriate for CdTe. According to this classification, p-CdTe polycrystalline thin film would not likely have dopants, because no acceptor levels typically can be found in CdTe thin film with activation so close to the valence band edge.
Shallow Dopants and Non-Shallow Dopant Classification
Classification of impurity/defect states as either dopants or deep levels based on equation (1) may not be appropriate for wide bandgap materials, including CdTe, which may lack fully ionized shallow dopants. The shallow/non-shallow classification scheme addresses this by classifying impurity/defect states based on a probability of ionization. Following the laws of thermodynamics, the probabilities of ionization of a donor state and of an acceptor state are referred to the Fermi level EF. In this regard, the concentration of ionized donors ND+ and the concentration of ionized acceptors NA− can be expressed mathematically as follows:
                    {                                                                              N                  D                  +                                =                                                      N                    D                                    ⁢                                      1                                          1                      +                                                                        g                          D                                                ⁢                                                  exp                          ⁡                                                      (                                                                                                                            E                                  F                                                                -                                                                  E                                  D                                                                                            kT                                                        )                                                                                                                                                                                                                                        N                  A                  -                                =                                                      N                    A                                    ⁢                                      1                                          1                      +                                                                        g                          A                                                ⁢                                                  exp                          ⁡                                                      (                                                                                                                            E                                  A                                                                -                                                                  E                                  F                                                                                            kT                                                        )                                                                                                                                                                                                      (        2        )            
where gD and gA are the degeneracy of the donor and acceptor states, respectively, EA is the acceptor activation energy, ED is the donor activation energy, EF is the Fermi energy or level, k is the Boltzmann constant, T is absolute temperature in Kelvin, and the product of the Boltzmann constant k and the absolute temperature T is 0.0259 electron Volts (kT=0.0259 eV). The degeneracy of the donor states is 2 (gD=2) due to spin degeneracy, and the degeneracy of the acceptor states gA depends on the material. For tetrahedral cubic semiconductors, such as Si, GaAs, and CdTe, the degeneracy of acceptor states is 4 (gA=4). In addition to the contribution of spin degeneracy on the degeneracy of the acceptor states gA, the acceptor states also have the heavy hole and light hole degeneracy. E′D and E′A can be substituted for ED and EA, respectively, in equation (2), where E′D and E′A can be represented mathematically as follows:
                    {                                                                              E                  D                  ′                                =                                                      E                    D                                    -                                      kT                    ⁢                                                                                  ⁢                    ln                    ⁢                                                                                  ⁢                                          g                      D                                                                                                                                                                E                  A                  ′                                =                                                      E                    A                                    +                                      kT                    ⁢                                                                                  ⁢                    ln                    ⁢                                                                                  ⁢                                          g                      A                                                                                                                              (        3        )            By substituting E′D and E′A for ED and EA, respectively, in equation (2), the concentration of ionized donors and ionized acceptors can be simplified as follows:
                    {                                                                              N                  D                  +                                =                                                      N                    D                                    ⁢                                      1                                          1                      +                                              exp                        ⁡                                                  (                                                                                                                    E                                F                                                            -                                                              E                                D                                ′                                                                                      kT                                                    )                                                                                                                                                                                                              N                  A                  -                                =                                                      N                    A                                    ⁢                                      1                                          1                      +                                              exp                        ⁡                                                  (                                                                                                                    E                                A                                ′                                                            -                                                              E                                F                                                                                      kT                                                    )                                                                                                                                                                            (        4        )            
Using the above, impurity/defects states can be classified as shallow or non-shallow as follows:
                    {                                                            Donor                ⁢                                  {                                                                                    Shallow                                                                                                                                                        E                              D                              ′                                                        -                                                          E                              F                                                                                >                                                      3                            ⁢                            kT                                                                                                                                                >                                                      95                            ⁢                            %                            ⁢                                                                                                                  ⁢                            ionized                                                                                                                                                                                        Non                          ⁢                                                      -                                                    ⁢                          shallow                                                                                                                                                                                E                              F                                                        -                                                          E                              D                              ′                                                                                >                                                      3                            ⁢                            kT                                                                                                                                                <                                                      5                            ⁢                            %                            ⁢                                                                                                                  ⁢                            ionized                                                                                                                                                                                                                      Acceptor                ⁢                                  {                                                                                    Shallow                                                                                                                                                        E                              F                                                        -                                                          E                              A                              ′                                                                                >                                                      3                            ⁢                            kT                                                                                                                                                >                                                      95                            ⁢                            %                            ⁢                                                                                                                  ⁢                            ionized                                                                                                                                                                                        Non                          ⁢                                                      -                                                    ⁢                          shallow                                                                                                                                                                                E                              A                              ′                                                        -                                                          E                              F                                                                                >                                                      3                            ⁢                            kT                                                                                                                                                <                                                      5                            ⁢                            %                            ⁢                                                                                                                  ⁢                            ionized                                                                                                                                                                                                      (        5        )            
As shown in FIG. 1, the activation energy of the donor state D is closer to a band edge (e.g., Ev and Ec) than that of the acceptor state A. Yet the acceptor state is fully ionized with p=NA, and the donor state is only partially ionized with n<<ND.
Single-Level and Multi-Level State Classification
The single or multi-level state classification scheme proposes using “transition energy level” instead of “state” to describe the transition between two charge states of a localized impurity/defect. For example, an acceptor state is an impurity/defect with a transition from empty or neutral to occupied or negatively charged with an electron, which can be represented graphically as (o/−). A double acceptor is an impurity/defect with two possible transitions: from neutral to negative (o/−) and from negative to twice as negative (−/2−). Therefore, a localized impurity/defect may have a single transition level or multiple transition levels. The local charge neutrality (LCN) condition of a semiconductor with only single-level states can be expressed mathematically as follows:
                                                        N              V                        ⁢                          exp              ⁡                              (                                                                            E                      V                                        -                                          E                      F                                                        kT                                )                                              +                                    ∑              i                        ⁢                                          N                                  D                  i                                            ⁢                              1                                  1                  +                                      exp                    ⁡                                          (                                                                                                    E                            F                                                    -                                                      E                                                          D                              i                                                        ′                                                                          kT                                            )                                                                                                          =                                            N              C                        ⁢                          exp              ⁡                              (                                                                            E                      F                                        -                                          E                      C                                                        kT                                )                                              +                                    ∑              j                        ⁢                                          N                                  A                  i                                            ⁢                              1                                  1                  +                                      exp                    ⁡                                          (                                                                                                    E                                                          A                              j                                                        ′                                                    -                                                      E                            F                                                                          kT                                            )                                                                                                                              (        6        )            where EV is the valence band maximum (VBM), EC is the conduction band minimum (CBM), NV is the effective hole density in the valence band, and NC is the effective electron density in the conduction band. From equation (6), it is possible to solve the Fermi level, and with it the majority carrier density, using a numerical or graphical method.
FIGS. 2A-C show the activation energy of multi-level states. For example, referring to FIG. 2A, the double acceptor cadmium (Cd) vacancy in CdTe has a first activation energy 200 of 0.14 eV and a second activation energy 210 of 0.40 eV.
A generalized formulation of LCN equation of a semiconductor with single and double donors as well as single and double acceptors can be expressed mathematically as follows (for simplicity, the divalent amorphetic defect states are not included):
                                                        N              V                        ⁢                          exp              ⁡                              (                                                                            E                      V                                        -                                          E                      F                                                        kT                                )                                              +                                    ∑              i                        ⁢                                          N                                  D                  i                                            ⁢                              1                                  1                  +                                                                                    g                                                  D                          i                                                                          (                          0                          )                                                                                            g                                                  D                          i                                                                          (                          +                          )                                                                                      ⁢                                          exp                      ⁡                                              (                                                                                                            E                              F                                                        -                                                          E                                                              D                                i                                                                                                              kT                                                )                                                                                                                          +                                                                            ⁢                                          ∑                l                            ⁢                                                N                                      DD                                          l                      ⁢                                                                                                                                          ⁢                                                                                                                              g                                                      DD                            l                                                                                (                            +                            )                                                                                                    g                                                      DD                            l                                                                                (                                                          2                              +                                                        )                                                                                              ⁢                                              exp                        (                                                                                                            E                              F                                                        -                                                          E                                                              DD                                l                                                                                            (                                                                  2                                  +                                                                      /                                    +                                                                                                  )                                                                                                              kT                                                )                                                              +                    2                                                        1                    +                                                                                            g                                                      DD                            l                                                                                (                            +                            )                                                                                                    g                                                      DD                            l                                                                                (                                                          2                              +                                                        )                                                                                              ⁢                                              exp                        (                                                                                                            E                              F                                                        -                                                          E                                                              DD                                l                                                                                            (                                                                  2                                  +                                                                      /                                    +                                                                                                  )                                                                                                              kT                                                )                                                              +                                                                                            g                                                      DD                            l                                                                                (                            0                            )                                                                                                    g                                                      DD                            l                                                                                (                                                          2                              +                                                        )                                                                                              ⁢                                              exp                        [                                                                              2                            ⁢                                                          (                                                                                                E                                  F                                                                -                                                                  E                                                                      DD                                    l                                                                                                        (                                                                          2                                      +                                                                              /                                                                                                                                                                  ⁢                                        0                                                                                                              )                                                                                                                              )                                                                                kT                                                ]                                                                                                                                =                                            N              C                        ⁢                          exp              ⁡                              (                                                                            E                      F                                        -                                          E                      C                                                        kT                                )                                              +                                    ∑              j                        ⁢                                          N                                  A                  j                                            ⁢                              1                                  1                  +                                                                                    g                                                  A                          j                                                                          (                          0                          )                                                                                            g                                                  A                          j                                                                          (                          -                          )                                                                                      ⁢                                          exp                      (                                                                                                    E                                                          A                              j                                                                                -                                                      E                            F                                                                          kT                                            )                                                                                                    +                                    ∑              m                        ⁢                                          N                                  AA                  m                                            ⁢                                                                                                                  g                                                  AA                          m                                                                          (                          -                          )                                                                                            g                                                  AA                          m                                                                          (                                                      2                            -                                                    )                                                                                      ⁢                                          exp                      (                                                                                                    E                                                          AA                              m                                                                                      (                                                                                                -                                                                      /                                    2                                                                                                  -                                                            )                                                                                -                                                      E                            F                                                                          kT                                            )                                                        +                  2                                                  1                  +                                                                                    g                                                  AA                          m                                                                          (                          -                          )                                                                                            g                                                  AA                          m                                                                          (                                                      2                            -                                                    )                                                                                      ⁢                                          exp                      (                                                                                                    E                                                          AA                              m                                                                                      (                                                                                                -                                                                      /                                    2                                                                                                  -                                                            )                                                                                -                                                      E                            F                                                                          kT                                            )                                                        +                                                                                    g                                                  AA                          m                                                                          (                          0                          )                                                                                            g                                                  AA                          m                                                                          (                                                      2                            -                                                    )                                                                                      ⁢                                          exp                      [                                                                        2                          ⁢                                                      (                                                                                          E                                                                  AA                                  m                                                                                                  (                                                                                                            0                                      /                                      2                                                                        -                                                                    )                                                                                            -                                                              E                                F                                                                                      )                                                                          kT                                            ]                                                                                                                              (        7        )            where subscript DD implies double donor, and implies AA double acceptors.Single Atomic Configuration and Multiple Atomic Configuration Classification
Divalent states, such as Cd vacancies (VCd) in CdTe, have multiple transition energy levels, but a single atomic configuration with the same energy of formation. Another category of multi-level states is the multiple transition energy levels, which are due to multiple atomic configurations. For example, an impurity may have atomic configuration a with transition energy level Ea, and atomic configuration b with transition energy level Eb. The ratio of occupation of the impurity in configuration a and b is determined by Boltzmann distribution as follows:
                                          N            a                                N            b                          =                  exp          ⁡                      (                          -                                                Δ                  ⁢                                                                          ⁢                                      H                    a                                                                    Δ                  ⁢                                                                          ⁢                                      H                    b                                                                        )                                              (        8        )            
where ΔHa and ΔHb are the energies of formation of the configuration a and b, respectively.
Note that the transition from a to b, or vice versa, may incur an energy barrier to overcome, and the ratio of Na vs. Nb may be in a metastable state, different from eq. (8). The impurity with configuration a and configuration b can be treated as two independent states, not related to each other. The uncertainty of Na/Nb may impose severe challenges to the processing, stability, reliability, and proper operation of a device made of a semiconductor material with such multi-configurational impurity/defect states. An elevated temperature may trigger the change from one configuration to the other: from a shallow donor state to a deep level trap, from a donor state to an acceptor state, etc. An important example of multi configuration defect is copper (Cu) in CdTe. Cu can substitute Cd to form an acceptor CuCd, and Cu can also be an interstitial donor Cui.
To summarize, polycrystalline thin film CdTe is a non traditional semiconductor material with multiple, non-shallow, multi-level, multi-configuration, and self compensating localized defect states.
Double Acceptor Cd Vacancy in Polycrystalline CdTe Thin Film
Solar cells made of single crystalline semiconductor material usually have higher optic-electrical conversion efficiency than those made of polycrystalline thin film material. For example, single crystalline Si solar cell performs better than polycrystalline Si solar cell, which, in turn, has a higher conversion efficiency than amorphous Si thin film solar cell. CdS/CdTe solar cells are an exception. A great amount of R&D work has been done, with little or no success, in the effort of fabricating a single crystalline CdTe photovoltaic device, using such expensive facilities as MBE (molecular beam epitaxy) and MOCVD (metal organic chemical vapor deposition). A solar cell made of single crystalline CdTe performs far worse than its counterpart made of polycrystalline (PV) thin film. This experimental fact implies that the Cd vacancies incorporated more in CdTe thin film than in single crystal CdTe may play a critically important role in CdTe PV technology.
As shown in FIG. 3, a thorough search and first principle calculation reveals that potentially there are only three groups of p-dopants for CdTe: (a) the V-column element substitute of Te, a single acceptor, such as PCd, AsCd, and SbCd; (b) the Cd vacancy (VCd); a double acceptor; and (c) a noble metal substitute of Cd, a single acceptor, such as a copper (Cu) substitute of cadmium (Cd) (CuCd) and a silver (Ag) substitute of cadmium (Cd) (AgCd). The first group of acceptors cannot be formed in polycrystalline thin film CdTe, which has a high density of Cd vacancies. The energy of formation of the V-column impurity atom substitute of Cd by falling into the Cd vacancy is much favorable than that of V-column impurity atom to replace the Te in the crystal structure.
The double acceptor VCd, which represents a second potential p-dopant for CdTe, naturally exists in low cost CdTe polycrystalline thin film, especially on the grain boundaries. The first ionization energy level of VCd is 0.13 eV (calculated) or 0.15 eV (experimental), which make the Cd vacancy a viable p-dopant. However, its second ionization energy level (0.21 eV calculated, and 0.6-0.9 eV experimental) makes VCd a Shockley-Read-Hall (SRH) recombination center, which leads to dark current in PV diodes. Therefore, VCd is not an ideal p-dopant for CdTe.
The third group of potential p-dopant CdTe is a noble metal substitute of Cd, especially CuCd. CdTe thin film typically uses low cost 5N tellurium, which, either as a byproduct of copper refinery or a raw material from independent tellurium mine, may have up to 2×10−6 (2 ppm) Cu impurity content. In addition, as part of the back contact material, Cu diffuses into the CdTe thin film. CuCd is a single level acceptor with calculated ionization or activation energy of 0.22 eV, and experimental value of 0.15 eV (by photoluminescence), 0.3˜0.4 eV (rendered by Hall effect measurement), or 0.35 eV (by using deep level transient spectroscopy or DLTS). Although not ideally shallow, as a p-dopant the single level acceptor CuCd will not introduce the same amount of SRH recombination centers as the double acceptor VCd does.